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EEG/MEG source reconstruction

EEG/MEG source reconstruction. Jean Daunizeau Vladimir Litvak Wellcome Trust Centre for Neuroimaging 9 / 05 / 2008. Outline. Introduction Forward problem Inverse problem Bayesian inference applied to the EEG/MEG inverse problem Conclusion. Outline. Introduction Forward problem

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EEG/MEG source reconstruction

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  1. EEG/MEGsource reconstruction Jean Daunizeau Vladimir Litvak Wellcome Trust Centre for Neuroimaging 9 / 05 / 2008

  2. Outline Introduction Forward problem Inverse problem Bayesian inference applied to the EEG/MEG inverse problem Conclusion

  3. Outline Introduction Forward problem Inverse problem Bayesian inference applied to the EEG/MEG inverse problem Conclusion

  4. Introduction EEG/MEG and neuroimaging MRI MEG EEG invasivity weak strong OI EEG 20 spatial resolution (mm) MEG SPECT 15 OI PET 10 fMRI sEEG 5 MRI(a,d) 1 10 102 103 104 105 temporal resolution (ms)

  5. Introduction forward/inverse problems : definitions  Forward problem = modelling • Inverse problem = estimation of the model parameters

  6. Outline Introduction Forward problem Inverse problem Bayesian inference applied to the EEG/MEG inverse problem Conclusion

  7. Forward problem physical model of bioelectrical activity current dipole

  8. Forward problem the general linear model noise dipoles gain matrix measurements Y = KJ + E1

  9. Outline Introduction Forward problem Inverse problem Bayesian inference applied to the EEG/MEG inverse problem Conclusion

  10. Inverse problem an ill-posed problem • Jacques Hadamard (1865-1963) • Existence • Unicity • Stability

  11. Inverse problem an ill-posed problem • Jacques Hadamard (1865-1963) • Existence • Unicity • Stability

  12. Inverse problem cortically distributed current dipoles

  13. Inverse problem regularization Spatial and temporal constraints Adequacy with other modalities Data fit data fit constraint (regularization term) W = I : minimum norm method W =Δ : LORETA (maximum smoothness)

  14. Outline Introduction Forward problem Inverse problem Bayesian inference applied to the EEG/MEG inverse problem Conclusion

  15. Bayesian inference principle posterior pdf likelihood prior pdf model evidence

  16. Bayesian inference hierarchical generative model sensor level source level Q : (known) variance components (λ,μ) : (unknown) hyperparameters

  17. Bayesian inference hierarchical generative model λ1 λq J μ1 Y μq

  18. Bayesian inference SPM implementations IID COH prior covariance structure ARD/GS generative model M

  19. Outline Introduction Forward problem Inverse problem Bayesian inference applied to the EEG/MEG inverse problem Conclusion

  20. Conclusion at the end of the day… Individual reconstructions in MRI template space L R SPM machinery RFX analysis p < 0.01 uncorrected R L

  21. Conclusion summary • EEG/MEG source reconstruction: 1. forward problem; 2. inverse problem (ill-posed). • Prior information is mandatory to solve the inverse problem. • Bayesian inference is well suited for: 1. introducing such prior information… 2. … and estimating their weight wrt the data 3. providing us with a quantitative feedback on the adequacy of the model.

  22. Many thanks to Karl Friston, Stephan Kiebel, Jeremie Mattout

  23. Bayesian inference expectation-maximization (EM) average over J model associated with F generative model M

  24. Bayesian inference expectation-maximization (EM) M-step E-step EM / ReML algorithm

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